Counting Primes Rationally And Irrationally

Abstract

The recent technique for estimating lower bounds of the prime counting function π(x)=#{p ≤ x: p prime} by means of the irrationality measures $μ(ζ(s)) \geq 2$ of special values of the zeta function claims that $π(x) \gg \log \log x/\log \log \log x$